MathDB

Unit circle

Source: May Olympiad (Olimpiada de Mayo) 1999

February 26, 2018

geometry

Problem Statement

In a unit circle where

O

is your circumcenter, let

A

and

B

points in the circle with

\angle BOA = 90

. In the arc

AB

(minor arc) we have the points

P

and

OB

such that

PQ

is parallel to

AB

. Let

X

and

Y

be the points of intersections of the line

PQ

with

OA

and

OB

respectively. Find the value of

PX^2 + PY^2

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